Expectation value question

kasse · 2008-11-16T21:57:13+00:00

If \Psi (x,t) = \psi (x) g(t), should I then use \Psi or \psi when calculating and ?

Thread starter kasse
Start date Nov 16, 2008
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Expectation Expectation value Value

In summary, the expectation value is a mathematical concept used to represent the average value of a random variable or measurement in statistics and quantum mechanics. It is calculated by multiplying each possible outcome by its probability and summing the results in statistics, and by taking the integral of the product of the wave function and the operator in quantum mechanics. The expectation value serves as a measure of central tendency and can identify outliers in a dataset. It can be negative if the possible outcomes have both positive and negative values with non-symmetrical probabilities. However, it is not always a precise prediction as individual outcomes may vary significantly from this value, and in quantum mechanics, it may not correspond to any actual measurement outcome.

Nov 16, 2008

kasse

If [tex]\Psi (x,t) = \psi (x) g(t)[/tex], should I then use [tex]\Psi[/tex] or [tex]\psi[/tex] when calculating [tex]<p>[/tex] and [tex]<p ^2>[/tex]?

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Nov 17, 2008

PullMeOut

you should use the [tex]\Psi(x,t)[/tex] while calculating expectation value
it should include t parameter

1. What is an expectation value?

The expectation value is a mathematical concept used in statistics and quantum mechanics to represent the average value of a random variable or the average outcome of a measurement, respectively.

2. How is an expectation value calculated?

In statistics, the expectation value is calculated by multiplying each possible outcome by its probability and summing the results. In quantum mechanics, it is calculated by taking the integral of the product of the wave function and the operator representing the quantity being measured.

3. What is the significance of the expectation value?

The expectation value provides a way to estimate the average outcome of a random variable or measurement. It also serves as a measure of central tendency and can help identify outliers in a dataset.

4. Can the expectation value be negative?

Yes, the expectation value can be negative. This can occur if the possible outcomes have both positive and negative values, and the probabilities associated with these outcomes are not symmetrical.

5. Is the expectation value always a precise prediction?

No, the expectation value is not always a precise prediction. It represents the average outcome of a random variable or measurement, but individual outcomes may vary significantly from this value. Additionally, in quantum mechanics, the expectation value may not correspond to any actual measurement outcome.